What is the Least Common Multiple of 1638 and 1647?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 1638 and 1647 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1638 and 1647, than apply into the LCM equation.

GCF(1638,1647) = 9
LCM(1638,1647) = ( 1638 × 1647) / 9
LCM(1638,1647) = 2697786 / 9
LCM(1638,1647) = 299754

Least Common Multiple (LCM) of 1638 and 1647 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1638 and 1647. First we will calculate the prime factors of 1638 and 1647.

Prime Factorization of 1638

Prime Factorization of 1647

Now multiplying the highest exponent prime factors to calculate the LCM of 1638 and 1647.

LCM(1638,1647) = 2¹ × 3³ × 7¹ × 13¹ × 61¹
LCM(1638,1647) = 299754